A short basis of the Stickelberger ideal of a cyclotomic field

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00135200" target="_blank" >RIV/00216224:14310/24:00135200 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/mcom/3863" target="_blank" >https://doi.org/10.1090/mcom/3863</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/mcom/3863" target="_blank" >10.1090/mcom/3863</a>

Result language
angličtina
Original language name
A short basis of the Stickelberger ideal of a cyclotomic field
Original language description
We exhibit an explicit short basis of the Stickelberger ideal of cyclotomic fields of any conductor, i.e., a basis containing only short elements. An element of the group ring Z[G], where G is the Galois group of the field, is said to be short if all of its coefficients in basis G are 0 or 1. As a direct practical consequence, we deduce from this short basis an explicit upper bound on the relative class number that is valid for any conductor. This basis also has several concrete applications, in particular for the cryptanalysis of the Shortest Vector Problem on Ideal Lattices.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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